1. Tutorial 1: Sensitivity analysis of an analytical function

2. Example: Analytical nonlinear function
Additive linear and nonlinear terms and one coupling term
Contribution to the output variance (reference values): X1: 18.0%, X2: 30.6%, X3: 64.3%, X4: 0.7%, X5: 0.2%
Tutorial 1: Sensitivity Analysis

3. Task description Parameterization of the problem Defining DOE scheme
Evaluation of DOE designs
Statistical post-processing of DOE
Approximation post-processing of DOE
Defining MOP search algorithm
Evaluation of MOP workflow
Statistical post-processing of MOP
Approximation post-processing of MOP
Reload results in Result Monitoring
Use Matlab as solver
Use Excel as solver
Use Excel plug-in to export data in optiSLang format
Tutorial 1: Sensitivity Analysis

4. Project manager Open the project manager Define project name1. 2. 3.
Open the project manager
Define project name
Create a new project directory
Copy optiSLang examples/Coupled_Function into project directory
Tutorial 1: Sensitivity Analysis

5. Parameterization of the problem1. 2. 3. 4. 5.
Start a new parametrize workflow (double click)
Define workflow name
Create a new problem specification
Enter problem file name
Tutorial 1: Sensitivity Analysis

6. Parameterization of the problem1. 2. 3.
Click “open file” icon in parametrize editor
Browse for the SLang input file coupled_function.s
Choose file type as INPUT
Tutorial 1: Sensitivity Analysis

7. Parameterization of the problem1. 2. 3.
Mark value of X1 in the input file
Define X1 as input parameter
Enter parameter name
Tutorial 1: Sensitivity Analysis

8. Parameterization of the problem1. 2.
Open parameter in parameter three
Enter lower and upper bounds
Set as default for other variables and repeat for X2 … X5 3.
Tutorial 1: Sensitivity Analysis

9. Parameterization of the problem1. 2. 3.
Click “open file” icon in parametrize editor
Browse for the SLang output file coupled_solution.s
Choose file type as OUTPUT
Tutorial 1: Sensitivity Analysis

10. Parameterization of the problem4. 2. 3. 1.
Mark output value in editor
Define Y as output parameter
Enter parameter name
Close parametrize editor
Tutorial 1: Sensitivity Analysis

11. Parameterization of the problem1. 2. 3.
Check parameter overview for inputs
Check parameter overview for outputs
Close overview
Tutorial 1: Sensitivity Analysis

12. Define Design Of Experiments (DOE)2. 1. 3. 4.
Start a new DOE workflow (double click)
Define workflow name
Define workflow identifier (working directory)
Enter problem file name
Tutorial 1: Sensitivity Analysis

13. Define Design Of Experiments (DOE)1. 2. 3. 4.
Enter solver call (slang –b coupled_function.s)
Enter number of parallel runs
Choose if design directories should be deleted
Start DOE workflow
Tutorial 1: Sensitivity Analysis

14. Generate DOE scheme Choose Latin hypercube sampling1. 2. 3.
Choose Latin hypercube sampling
Enter number of samples (50…100)
Generate samples
Close dialog and show samples 4.
Tutorial 1: Sensitivity Analysis

15. Generate DOE scheme Start evaluation of samples 1.
Tutorial 1: Sensitivity Analysis

16. Statistics post-processing3. 1. 5. 2. 4. 6.
Linear correlation matrix (In-In, In-Out, Out-In and Out-Out)
Quadratic correlation matrix (total values or difference to linear)
Histogram of input/output (select variable in 1.)
Anthill plot (select variables in 1.)
CoD/CoI values (linear: select in 1., quadratic: select in 2.)
Ranked linear or quadratic correlations of single response
Tutorial 1: Sensitivity Analysis

17. Statistics post-processing1. 1. 2.
Switch between CoD/CoI visualization
Extended correlation matrix (optiSLang 3.2)
Tutorial 1: Sensitivity Analysis

18. Statistics post-processing1. 2.
Statistical properties of single variable
Traffic light plot of response for given safety & failure limit (optiSLang 3.2)
Tutorial 1: Sensitivity Analysis

19. Statistics post-processing1. 2. 3.
Show development of correlation coefficients
Show design table
Export DOE to Excel
Tutorial 1: Sensitivity Analysis

20. Statistics post-processing1. 2.
Principal Component Analysis (PCA) of linear correlations
Parallel coordinates plot to show designs having an input/output within certain lower and upper bounds
Tutorial 1: Sensitivity Analysis

21. Statistics post-processing1. 2.
Significance filter for CoD/CoI
Manual filter for CoD/CoI
Tutorial 1: Sensitivity Analysis

22. Approximation post-processing3. 1. 2.
4a.
4b.
Anthill plot of parameter 1 and the response
Contour plot of approximation function in terms of parameter 1 and 2 (remaining are set to their mean) vs. the response
Surface plot of approximation function
Details about approximation settings and properties
Tutorial 1: Sensitivity Analysis

23. Approximation post-processing3.
4a.
4b.
Manual approximation settings:
Parameter subspace
Polynomial or MLS (exponential or regularized)
Basis polynomial, constant or density dependent influence
Transformation settings
Tutorial 1: Sensitivity Analysis

24. Meta-Model of Optimal Prognosis (MOP)2. 1. 3. 4. 5.
Start a new MOP workflow (double click)
Define workflow name
Define workflow identifier (working directory)
Choose DOE result file
Choose optional problem file
Tutorial 1: Sensitivity Analysis

25. Meta-Model of Optimal Prognosis (MOP)1. 4. 2. 3. 5.
CoP settings (sample splitting or cross validation)
Investigated approximation models
DCoP - accepted reduction in prediction quality to simplify model
Filter settings
Selection of inputs and outputs
Tutorial 1: Sensitivity Analysis

26. Meta-Model of Optimal Prognosis (MOP)
optiSLang console gives detailed information about the investigated models and obtained optimal CoP values
Tutorial 1: Sensitivity Analysis

27. Meta-Model of Optimal Prognosis (MOP)
Approximation post-processing automatically shows surface and contour plot of the two most important variables vs. the response
CoP values for single variables are shown
Tutorial 1: Sensitivity Analysis

28. Overview of different significance values
MOP/CoP close to reference values (detects optimal subspace automatically, represents nonlinear and coupling terms)
CoD, k=5 (all inputs)
CoI, k=5 (all inputs)
CoI, k=3 (manual)
CoP, k=3 (automatic)
Reference
Full model
75%
74%
97%
100% X1 2%
14%
18% X2
30%
28%
31% X3
41%
34%
39%
62%
64% X4 0% -
0.7% X5 1%
0.2%
Tutorial 1: Sensitivity Analysis

29. Reload DOE or MOP in Result Monitoring2. 1. 3.
Start a new Results Monitoring workflow (double click)
Define workflow name
Choose DOE or MOP result file
Start Post-Processing
Tutorial 1: Sensitivity Analysis

30. Tutorial 1: Use Matlab as solver

31. Use Matlab as solver Matlab input file: coupled_function.m1. 2. 3. 4.
Matlab input file: coupled_function.m
Input parameter definition
Function evaluation
Writing the result file
Exit Matlab execution!
Tutorial 1: Sensitivity Analysis

32. Use Matlab as solver Call Matlab from Windows: matlab_windows.bat1. 2. 3. 4. 5.
Call Matlab from Windows: matlab_windows.bat
Disable splash
Disable desktop
Disable java virtual machine
Minimize remaining command window
Wait until Matlab is terminated
Tutorial 1: Sensitivity Analysis

33. Use Matlab as solver Call Matlab from Linux: matlab_linux.sh1. 2. 3. 4. 5.
Call Matlab from Linux: matlab_linux.sh
Set empty display
Disable splash
Disable desktop
Disable java virtual machine
Wait until Matlab is finished
Tutorial 1: Sensitivity Analysis

34. Use Matlab as solver 1. 2.
Parameterize inputs in optiSLang from coupled_function.m
Parameterize output from coupled_solution.txt
Tutorial 1: Sensitivity Analysis

35. Use Matlab as solver 1. 2.
Open new DOE workflow and select “Run a script file”
Choose the batch script and start DOE process
Tutorial 1: Sensitivity Analysis

36. Tutorial 1: Use Excel as solver

37. Use Excel as solver 2. 1. 3.
Generate Excel file with all inputs in one row and all outputs in one column
Mark first input as inputParams
Mark first output as outputParams
Tutorial 1: Sensitivity Analysis

38. Use Excel as solver Show Macros Enter Macro name Create Macro 1. 2. 3.
Tutorial 1: Sensitivity Analysis

39. Use Excel as solver 1. 2.
In Visual Basic environment use import file feature
Import predefined macro file inout.bas
Tutorial 1: Sensitivity Analysis

40. Use Excel as solver inout module should be shown in the module list1. 1. 2.
inout module should be shown in the module list
Delete the empty default module
Tutorial 1: Sensitivity Analysis

41. Use Excel as solver The visual basic macro Input file name1. 2.
The visual basic macro
Input file name
Output file name
Tutorial 1: Sensitivity Analysis

42. Use Excel as solver Java script to run Excel in batch mode1.
Java script to run Excel in batch mode
Excel file name
Tutorial 1: Sensitivity Analysis

43. Use Excel as solver Batch script to run Excel java script1.
Batch script to run Excel java script
Call of java script with full path, modify path if necessary!
Tutorial 1: Sensitivity Analysis

44. Use Excel as solver Parameterize inputs in optiSLang from input.txt1. 2.
Parameterize inputs in optiSLang from input.txt
Parameterize output from output.txt
Tutorial 1: Sensitivity Analysis

45. Use Excel as solver 1. 2.
Open new DOE workflow and select “Run a script file”
Choose the batch script and start DOE process
Tutorial 1: Sensitivity Analysis

46. Tutorial 1: Use Excel plug-in

47. Use Excel plug-in Start the plug-in in Excel1. 2.
3b.
3a.
Start the plug-in in Excel
Mark input data including parameter names
Check parameter names and data array
Tutorial 1: Sensitivity Analysis

48. Use Excel plug-in Mark output data including parameter names
2b. 1.
2a.
Mark output data including parameter names
Check parameter names and data array
Tutorial 1: Sensitivity Analysis

49. Use Excel plug-in Choose design numbers1. 2.
Choose design numbers
Finish and save data in optiSLang *.bin file
Open *.bin in result monitoring workflow
Tutorial 1: Sensitivity Analysis